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We study the equality of the extremal Betti numbers of the binomial edgeideal $J_G$ and those of its initial ideal ${\rm in}(J_G)$ of a closed graph$G$. We prove that in some cases there is an unique extremal Betti number for${\rm in}(J_G)$ and as a consequence there is an unique extremal Betti numberfor $J_G$ and these extremal Betti numbers are equal

On the extremal Betti numbers of the binomial edge ideal of closed graphs